The ℓpᵖ norm of the Riesz–Titchmarsh transform for even integer pp

The long‐standing conjecture that for the norm of the Riesz–Titchmarsh discrete Hilbert transform is the same as the norm of the classical Hilbert transform, is verified when or , for . The proof, which is algebraic in nature, depends in a crucial way on the sharp estimate for the norm of a different variant of this operator for the full range of . The latter result was recently proved by the authors ( Duke Math. J . 168 (2019), no. 3, 471–504).